Ab initio Molecular Dynamics Simulations of the
Adsorption of H2 on Palladium Surfaces
Axel Groß
Institute of Theoretical Chemistry, University of Ulm, 89069 Ulm, Germany
E-mail: [email protected]
The interaction of hydrogen molecules with clean and hydrogen-precovered Pd surfaces was
studied using ab initio molecular dynamics simulations based on density functional theory.
In particular, the dependence of the adsorption probability on the hydrogen coverage and the
relaxation of hot hydrogen atoms after dissociation were addressed. The simulations unravel
the crucial role of the substrate degrees of freedom in the dissociative adsorption process.
1 Introduction
The interaction of hydrogen with metal surfaces has been one of the benchmark system
for the understanding of gas-surface dynamics1, 2. This is due to the fact that this system is
well-suited for both experimental as well as theoretical studies. Furthermore, the hydrogen
adsorption on metal surfaces is also relevant from a technological point of view, in particular in the context of hydrogen storage, but also with respect to hydrogenation reaction in
heterogeneous catalysis.
Because of the light mass of hydrogen, the dynamics of H2 adsorption on low-index
metal surfaces has mainly been studied using a quantum mechanical treatment on parameterized potential energy surfaces derived from density functional theory (DFT) calculations3, 4 . In these calculations, all six degrees of freedom of the H2 molecule were explicitly
considered, the substrate degrees of freedom, however, were kept frozen since otherwise
the calculations would have been computationally much too expensive. This was justified
by the large mass mismatch between hydrogen and metal atoms. In addition, comparisons between six-dimensional quantum and classical calculations showed that the role of
quantum effects in the hydrogen adsorption dynamics on surfaces is limited5, 6.
If more than six degrees of freedom are involved, quantum dynamical calculations are
computationally prohibitive. Furthermore, the parameterization of such high-dimensional
potential energy surfaces becomes quite cumbersome. Ab initio molecular dynamics
(AIMD) simulations of the adsorption dynamics represent an alternative approach. In these
simulations, the forces necessary to integrate the equations of motion are determined “on
the fly” by first-principles calculations. This does not require any parameterization of the
potential energy surfaces. However, up to recently AIMD simulations were restricted to a
small number of trajectories because of their high computational effort7, 8.
Previously, we had studied the adsorption and scattering of O2 /Pt(111) using ab initio
derived tight-binding molecular dynamics (TBMD) simulations9–11 . This method is about
three orders of magnitude faster than AIMD simulations, and it needs relatively little input
from ab initio total-energy calculations since the tight-binding Hamiltonian already takes
the quantum nature of bonding into account9. However, the TBMD method still involves
a fitting procedure which introduces a source of possible errors; this is true in particular, if
more than two different elements are included in the simulations.
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Fortunately, due to the increase in computer power and the development of more efficient algorithms it has now become possible to determine a statistically meaningful number of AIMD trajectories12 . In this contribution, this will be demonstrated using the H2
adsorption on precovered Pd surfaces and the relaxation of the hydrogen atoms after the
dissociation on clean surfaces as examples.
2 Theoretical Methods
Periodic DFT calculations were performed within the generalized gradient approximation
(GGA)13, 14 for the exchange-correlation functional using the VASP code15 . The atomic
cores were represented by ultrasoft pseudopotentials16 allowing a small cutoff energy of
200 eV in the expansion of the one-electron valence states in plane waves. The surface was
modelled by slabs of three to five layers for the (100) surface and five layers for the (111)
surface. The uppermost layers were allowed to move in the simulations in order to enable
recoil and energy transfer processes at the surface.
Adsorption probabilities were determined by averaging over at least 200 trajectories
with random initial lateral configurations and molecular
orientations
for one particular kip
√
netic energy. This leads to a statistical error of s(1 − s)/ 200 ≤ 0.035, where s is the
adsorption probability. All the substrate atoms were initially at rest, i.e., the initial surface
temperature corresponded to 0 K. The MD simulations were performed using the Verlet algorithm with a time step of 1 fs within the microcanonical ensemble. The parallel version
of the VASP code was written using a message-passing programming model relying on the
MPI library to deal with communications.
3 Hydrogen Dissociation on Hydrogen-Precovered Pd Surfaces
In a recent STM study addressing the formation of ordered hydrogen layers on Pd(111), it
was found that hydrogen molecules impinging on an almost complete hydrogen overlayer
did not adsorb dissociatively in hydrogen dimer vacancies17, 18. Instead, aggregates of
three or more vacancies were required for the dissociation of H2 . As a consequence, it was
speculated that the accepted notion that two empty sites are needed for the dissociative
adsorption of diatomic molecules might not be correct17, 19. However, a subsequent DFT
study demonstrated that the dissociative adsorption of H2 in a hydrogen dimer vacancy
is still exothermic20. Nevertheless, because of repulsive interactions the presence of the
hydrogen overlayer leads to the formation of small energetic barriers. Thus the dissociative
adsorption of H2 on hydrogen-precovered Pd(111) is no longer spontaneous but becomes
an activated process by the so-called poisoning effect of the hydrogen overlayer.
Still, the H2 adsorption process requires the dissipation of more than 1 eV20 . It has been
proposed that the energy transfer to substrate phonons or electron hole-pair excitations
could be suppressed due to surface stiffening or the modification of the electronic band
structure, respectively, caused by the hydrogen overlayer21. The magnitude of these effects,
however, could not be assessed so far. Therefore we have addressed the dynamics of
the H2 dissociative adsorption on hydrogen-precovered Pd surfaces by performing AIMD
simulations.
In a first step, we used a small initial kinetic energy of 0.02 eV as in the STM experiments. And indeed, we did not find any single adsorption event in a hydrogen dimer
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0.8
S(Θ) = S(0) (1 - Θ)
Pd(111)
0.8
4
Impinging H2 molecule (eV)
Hydrogen overlayer (eV)
Pd substrate atoms (eV)
(b)
2
0.6
0.4
Ekin = 0.1 eV
H2 distance (Å)
0.6
3
0.4
2
0.2
1
3VH
0.2
2V
0.0
0.00
3VT
0.25
0.50
0.75
Hydrogen coverage ΘH
1.00
0.0
0
1000
2000
3000
4000
H2 distance from the surface (Å)
Pd(100)
fixed Pd and H substrate atoms
fixed Pd substrate atoms
fixed H substrate atoms
S(Θ) = S(0) (1 - Θ)
(a)
Kinetic energy (eV)
Relative sticking probability S(Θ)/S(0)
1.0
0
Run time (fs)
Figure 1. Dissociative adsorption of hydrogen on hydrogen-covered Pd(100) and Pd(111). a) Calculated sticking
probability as a function of hydrogen coverage θH for an initial kinetic energy of 0.1 eV. 2V, 3VH and 3VT
denote the dimer vacancy and the trimer vacancy centred around a Pd hollow and a Pd top site, respectively. b)
Energy redistribution and H2 centre of mass distance from the surface along a particular trajectory for θH = 5/9.
vacancy (2V) on Pd(111) within a (3 × 3) surface geometry, thus confirming the experiment17 and providing an explanation for the experimental findings: At the low temperatures
of 70 K used in the experiment17 the impinging H2 molecules had too little kinetic energy
to cross the dissociation barrier.
At higher kinetic energies, however, H2 molecules can adsorb dissociatively in a dimer
vacancy on hydrogen-covered Pd(111). This is shown in Fig. 1a where the sticking probabilities for both Pd(111) and Pd(100) are plotted as a function of the hydrogen coverage
normalized to the value at the corresponding clean Pd surfaces for an kinetic energy of
0.1 eV. On Pd(111), a small, but non-vanishing relative adsorption probability of 0.05 is
found in the dimer vacancy (2V). At the trimer vacancies on Pd(111) centred either around
a hollow site (3VH ) or a Pd top site (3VT ), the adsorption probability is at least twice as
large as on the dimer vacancy (2V). Since the area of the trimer vacancy is only larger
by 50% compared to the dimer vacancy, this indicates that it is not only the area of the
vacancies that determines the adsorption probability.
In Fig. 1a, two curves corresponding to S(ΘH ) = S(0)(1 − ΘH ) and S(ΘH ) =
S(0)(1 − ΘH )2 are included which would correspond to the sticking probability if it was
determined by pure site-blocking requiring one or two empty sites, respectively. At low
and intermediate coverages, the sticking probability of H2 at Pd(100) is significantly larger
than predicted from a simple site-blocking picture, in particular for ΘH = 0.5. Running
additional AIMD trajectories with the substrate kept fixed reveals that it is the energy transfer from the impinging H2 molecule to the substrate and the rearrangement of the substrate
atoms that lead to this enhanced sticking probability compared to pure site blocking12.
These effects overcompensate the poisoning of the H2 dissociation caused by the presence
of the hydrogen overlayer atoms.
A rather surprising result is, however, that both the motion of the hydrogen atoms and
the Pd atoms contribute to the high sticking probability at the precovered surfaces, as the
simulations with only fixed Pd atoms and with only fixed hydrogen overlayer atoms show
(see the results in Fig. 1a for θH = 1/2). Not only energy transfer processes alone but also
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a) 720 fs
b) 2836 fs
c) 3360 fs
Figure 2. Snapshots of the AIMD trajectory of H2 impinging on hydrogen-precovered Pd(100) whose energy
distribution is plotted in Fig. 1b. The initial hydrogen coverage is θH = 5/9 within a (3 × 3) surface periodicity,
i.e., there are four hydrogen vacancies in the surface unit cell.
substrate recoil and relaxation effects in the highly corrugated potential energy surface
enhance the sticking probability of H2 molecules, as a detailed analysis of the adsorption
dynamics indicates.
Details of the energy transfer along a particular trajectory for an initial hydrogen coverage of θH = 5/9 are presented in Fig. 1b, and three snapshots along this trajectory within
the (3 × 3) periodicity are presented in Fig. 2. This specific example furthermore demonstrates that AIMD simulations do not only yield statistically reliable reaction probabilities,
but also allow for valuable microscopic insights into the dissociative adsorption dynamics.
At the hydrogen-covered Pd(100) surface, the impinging H2 molecules do not necessarily either immediately dissociate or scatter back into the gas phase. In fact, there exists
a weakly bound molecular precursor state above the top sites which becomes stabilized
due to the poisoning effects of the pre-adsorbed hydrogen atoms, very similar to the one
already identified at the hydrogen-covered stepped Pd(210) surface22, 23. This state has not
been identified experimentally yet, however, it should be detectable at low surface temperatures by, e.g., isotope exchange experiments since it is bound by 0.1 eV. In the case of the
particular trajectory considered in Fig. 1b, after impinging on the surface the H2 molecule
becomes first trapped for more than 2 ps in the molecular precursor state about 2 Å above
a Pd atom (Fig. 2a).
At about 2.5 ps, one of the two hydrogen atoms enters the four-fold atomic adsorption
site which is associated with an energy gain of about 0.5 eV. This energy is first taken up
by the corresponding hydrogen atom but is then rapidly transfered to both the hydrogen
overlayer and the Pd substrate atoms. The other hydrogen atom remains at a bridge site
configuration where is stays for about 0.8 ps (Fig. 2b). The additional bridge-site hydrogen
atom can actually move in an exchange mechanism24 which is what happens after 3.3 ps:
the bridge-site hydrogen atom replaces one of the adsorbed hydrogen atoms at an adjacent four-fold hollow sites which is then pushed up to an adjacent empty four-fold hollow
site so that eventually all hydrogen atoms end up in the most favourable adsorption sites.
However, the replaced hydrogen atom can also end up in another bridge-site configuration
which corresponds to an exchange-diffusion of this hydrogen species.
Recently, there has been a renewed interest in the hydrogen absorption in metals25 in
the context of the hydrogen technology. It is important to realize that hydrogen storage still
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a) 310 fs
b) 415 fs
c) 760 fs
Figure 3. Snapshots of a AIMD trajectory of H2 impinging on hydrogen-precovered Pd(100) with a kinetic
energy of 1.0 eV. Initially, there is a hydrogen dimer vacancy, i.e., the coverage is θH = 7/9 within the (3 × 3)
surface periodicity.
remains a problem26. Experiments showed that on Pd hydrogen first adsorbs on the surface
before bulk absorption starts27 . DFT calculations have confirmed this picture by showing
that hydrogen subsurface absorption is energetically less favourable than adsorption on
the surface23 ; furthermore, the penetration into the Pd bulk is hindered by a barrier of
considerable height25 .
In the AIMD simulations of the hydrogen interaction with hydrogen-precovered Pd
surfaces with an initial kinetic energy of 0.1 eV, we did not find any subsurface adsorption
events. This is due to the fact that the subsurface penetration corresponds to a rare event
because of its activated nature. In order to obtain hydrogen penetration events, we ran trajectories with the unrealistically high initial kinetic energy of 1.0 eV so that the chance is
higher that the hydrogen atoms have enough energy to overcome the barrier towards subsurface adsorption. And indeed, thus we observed several hydrogen subsurface adsorption
events. Interestingly, most of these events involved a concerted motion of hydrogen atoms
which is illustrated in Fig. 3.
Initially, one of the two atoms of the impinging H2 molecule enters a four-fold hollow
site while the other one is again trapped in a bridge configuration (Fig. 3a), as already
depicted in Fig. 2b. Note that because of the high initial kinetic energy of 1.0 eV there
is a large amount of excess energy available which is mainly transfered to the hydrogen
overlayer atoms. After about 400 fs, there is a concerted motion of the hydrogen bridgesite atom and the H atom to its right in Fig. 3b at the adjacent four-fold hollow site. The
bridge-site atom replaces the other hydrogen atom, but this time the other atom does not
pop up to the surface, but is rather pushed into the subsurface layer. Thus it seems that
the subsurface penetration is facilitated when more than one hydrogen atom are involved
in this process. The elucidation of the mechanism of the hydrogen subsurface adsorption
certainly requires further studies.
After the one hydrogen atom has gone subsurface, the remaining hydrogen atoms on the
surface are still energetically hot which is reflected in the large amplitudes of the vibrational
motion of the hydrogen atoms with respect to their equilibrium positions that are visible in
Figs. 3b and c. Through interatomic collisions, one of the hydrogen overlayer atoms in fact
gains enough kinetic energy to cross the diffusion barrier and hops into the neighbouring
vacancy site (Fig. 3c).
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(a)
1.0
12
0.9
10
8
0.8
7
0.7
6
0.6
5
0.5
4
0.4
3
0.3
2
0.2
1
0.1
0
0
0.0
200 400 600 800 1000 1200 1400 1600 1800 2000
y-coordinate (Å)
Distance (Å)
9
H-H distance
H displacement
Kin. energy of H2
Kin. energy of Pd atoms
Energy (eV)
10
(b)
8
6
4
2
0
-2
-4
-8
-6
-4
-2
0
2
4
6
8
x-coordinate (Å)
Run time (fs)
Figure 4. Calculated relaxation of dissociated H2 molecules on clean Pd(100) within a (6 × 6) surface unit cell.
a) H-H distance, the displacement of the single H atoms from their initial lateral position, the kinetic energy of
the H2 molecules and of the Pd substrate as a function of the run time averaged over 80 AIMD trajectories with
an initial H2 kinetic energy of 200 meV. b) Illustration of a trajectory of the hydrogen atoms after dissociation.
The total run time was 2 ps. The surface unit cell of the simulations is indicated by the dashed blue line.
4 Relaxation Dynamics of Dissociated H2 Molecules
So far we have focused on the dissociation of H2 on hydrogen-covered Pd surfaces. We
were only interested in the question whether H2 dissociates on Pd or not, but we did not
consider the fate of the hydrogen atoms after the dissociation. However, directly after
the dissociation when the atoms enter the atomic adsorption wells, they gain a significant
amount of energy. For H2 /Pd, this amounts to about 1 eV for the two H atoms together
and thus gives rise to the formation of “hot” atoms, i.e., atoms with energies much larger
than thermal energies. These atoms can use their kinetic energy in order to travel along the
surface. The mean free path of these hot atoms is for example relevant for catalytic reactions on surfaces since it determines whether adjacent reactants can react directly after the
dissociative adsorption of one of the species or whether some diffusive motion is required
before any further reaction can occur. So far, simulations addressing the relaxation of hot
atoms after dissociation have only modelled the motion of single atoms with initial velocities considered to be typical for dissociation fragments directly after the bond-breaking
process28, 29. We have decided to model the full relaxation process including the interaction of the two fragments after the dissociation. We have therefore run AIMD trajectories
of the dissociation of H2 on clean Pd(100). In order to minimize the interaction of the
hot hydrogen atoms with their periodic images, we have chosen a large (6 × 6) surface
unit cell. To reduce the computational cost, only three Pd layers were considered but test
calculations with five Pd layers yield hardly modified results.
Figure 4a shows the mean H-H distance and the mean displacement of the single H
atoms as a function of time averaged over 80 AIMD trajectories whereas in Fig. 4b one
specific trajectory is displayed that was run for 2 ps. The trajectory shows that the single
hydrogen atoms visit several surface sites. In this particular trajectory, the hydrogen atoms
approach each other again after an initial increase in the interatomic distance. At a certain
time, they are moving towards adjacent adsorption sites before they separate again. This
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shows that the mutual interaction can be important for the hot atom movement.
As for the mean distance between the two H atoms, after about 1.5 ps it reaches a value
of about 8.5 Å and does not increase any further. This corresponds to about three Pd lattice
units. It should be noted that the root mean square deviation in the H-H distance saturates
at about ±4 Å, however, single trajectories show a maximum H-H distance of more than
20 Å. In Fig. 4a, also the kinetic energies of the hydrogen and the Pd atoms, respectively,
are plotted. At about 100 fs, the hydrogen atoms gain on the average about 700 meV when
they enter the atomic adsorption well. This energy is then transfered from the hydrogen
atoms to the Pd substrate atoms. When the mean H-H distance does not change any more,
i.e., after 1.5 ps, the hydrogen atoms have only about 250 meV of kinetic energy left which
corresponds rather closely to the diffusion barrier for H atoms on Pd(100).
These results demonstrate that AIMD simulations are well-suited in order unravel details of reaction dynamics at surfaces that are not accessible by experiment.
Acknowledgments
These calculations were made possible through a grant of computer time at the John von
Neumann Institute for Computing in Jülich.
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